The magnitude of electric field `vecE` in the annular region of a charged cylindrical capacitor.

Options

A. (a) is same throughout
B. (b) is higher near the outer cylinder than near the inner cylinder
C. (c) varies as `1//r`, where r is the distance from axis
D. (d) varies as `1//r^2` where r is the distance from the axis.

Answer

C

Explanation

Let `lambda` be the charge per unit length. Let us consider a Gaussian surface (dotted cylinder).
Applying Gauss's law
`phi=ointvecE.vec(ds)=(lambdal)/(epsilon_0)`

For the flat portions of Gaussian surface, the angle between electric field and surface is `90^@`. Hence flux through flat portions is zero.
The angle between `vecE` and `vec(ds)` is `0^@` (for curved surface)
`implies E int ds =(lambdal)/(epsilon_0)impliesExx2pirl=(lambdal)/(epsilon_0)`
`implies E=(lambda)/(2piepsilon_0r)impliesE prop 1/r`